A Bo-Based Method For Parameter Tuning In Voltage Controlled Ders To Improve Flexibility Area At Tso-Dso Interface

The rapid proliferation of aggregated flexible resources in active distribution systems (ADSs) calls for accurate estimation of the flexibility area (FA) at the transmission system operator–distribution system operator (TSO–DSO) interface to improve operational coordination. Meanwhile, voltage control plays a critical role in maintaining both economic and secure grid operation. However, the relationship between voltage control parameters and the FA metric is highly nonlinear and analytically intractable, as inverter droop coefficients and other control parameters interact with network constraints and distributed energy resource (DER) operating conditions in a coupled manner. To address this challenge, this paper proposes a Bayesian optimization (BO)-based framework that systematically tunes voltage support parameters to maximize the FA potential. The main contributions are threefold: (1) a cross-layer optimization paradigm that links inverter-level droop control with systemlevel FA characteristics, revealing how voltage control curves shape interface power flow dynamics; (2) a reformulated FA estimation process in which the Interval-Constrained Power Flow (ICPF) model, embedded with droop-control operations, is cast as a Bayesian black-box problem solved efficiently via Gaussian process surrogates with a tile-coding kernel; and (3) a composite performance index, namely the Secure Area–Cost Flexibility (SeCoF), which jointly quantifies the trade-off between flexibility enhancement and operational cost. Case studies on modified IEEE 13-bus and IEEE 37-bus distribution systems demonstrate the effectiveness, robustness, and scalability of the proposed method in improving both technical flexibility and economic performance under realistic operational constraints.